Mr. Trump falsely claimed that his tax cuts, which he called “the most significant in history,” were the first “in close to 40 years.”

President Bill Clinton signed the Taxpayer Relief Act of 1997. President George W. Bush enacted two major tax cuts in 2001 and 2003. The stimulus passed under Mr. Obama included hundreds of billions of dollars in tax cuts, and he later extended the Bush tax cuts with the American Taxpayer Relief Act of 2012.

Mr. Reagan’s 1981 tax cut, Mr. Obama’s stimulus package and extensions of Mr. Bush’s tax cuts would all place ahead of Mr. Trump’s tax cut as a share of the economy and in inflation-adjusted dollars.

Mr. Trump’s claim that “there’s never really been a businessman or businessperson elected president” is wrong.

Several presidents have owned, operated or worked in the field of business.

Looking further back, George Washington, James Madison and James Monroe all owned plantations.

Mr. Trump’s claims about minority unemployment levels could use some context.

Mr. Trump is right that the unemployment rates for women and minorities are at or near historic lows. But it’s worth noting that these rates had been steadily declining for years by the time he took office.

For black Americans, the unemployment rate of 6.8 percent in December was the lowest ever recorded, according to the latest monthly data that is available from the Bureau of Labor Statistics. It had already decreased to 7.8 percent in January 2017 from over 15 percent in 2010.

The December figures also do not reflect a significantly different racial unemployment gap. The black unemployment rate has consistently been double that of the white unemployment rate, and it remained at that level in December.

The Latino unemployment rate declined to 4.9 percent in December from 5.9 percent in January 2017, the second lowest — not the lowest, as Mr. Trump said — on record. It reached 4.8 percent in June, October and November 2017, as well as in October 2006 under George W. Bush.

The 4.0 percent unemployment rate for women in December is among the lowest in 17 years, as Mr. Trump said. It was lower in October at 3.9 percent, down from 4.8 percent in January 2017.

Mr. Trump is right. Thestock market has “added more than $7 trillion in new wealth since my election.” But the gains are not widely shared.

Mr. Trump is most likely referring to the rise in the Wilshire 5000 Index, a widely used metric. The index grew to 29,431.74 on Wednesday, from 22,165.78 points on Election Day 2016, according to the Federal Reserve Bank of St. Louis, a gain of more than 7,200 points. A single point on the index represents $1.15 billion, so the market has added $8.3 trillion since Mr. Trump’s election.

But these gains in wealth have disproportionally benefited Americans by income bracket. Roughlyhalf of Americans do not own stock directly or in retirement accounts and mutual funds, and the richest 10 percent of households controlled 84 percent of the total value of stocks, a recent study by the nonpartisan National Bureau of Economic Research estimated.

Mr. Trump is right that coalition forceshave “retaken almost 100 percent of the territory” once held by the Islamic State, part of which occurred under Mr. Obama.

At its peak in January 2015, the jihadist group controlled 35,000 square miles of territory in the Middle East. By the time Mr. Trump took office in January 2017, their holdings had shrunk to about 23,000 square miles. It further dwindled to 2,500 square miles in January 2018, according to IHS Markit, a research firm that has tracked territory held by the Islamic State.

Many have said they will give one-time employee bonuses of $1,000 to $2,000. According to the list, only one, a private insurance company, announced $3,000 bonuses for 700 employees in a news release on Dec. 21, the day before Mr. Trump signed the tax bill.

It’s worth noting that most of these businesses are financial institutions and, as my colleague Jim Tankersley has reported, “The payouts to workers reflect a small slice of the windfall that banks large and small are in line to receive.”